function NonLinReg()
close all
global P N

I=[50; 150; 250; 350];
f=[-1845; -456; 1277; 2047];
DIM = 4;
B = 20;
P = zeros(DIM,2);

P(:,1) = I';
%P(:,2) = 2^B*sin(P(:,1)*pi/2/DIM);
P(:,2) = f;


N = 3;
c0 = ones(1,N+1);
%c0 = [.01 .01 .001 .001 .1 .1];


[c, res] = lsqnonlin(@Residuum,c0);

fprintf('res=%.6e\n',res);
fprintf('c=%.6e\n',c);

%h = (max(P(:,1))-min(P(:,1)))/(DIM-1);
%xx=min(P(:,1)):h:max(P(:,1));
yy=Ansatzfunktion(P(:,1),c);
plot(P(:,1),yy,'k-',P(:,1),P(:,2),'ro');
figure(2)
a=10;
L=length(yy)-a;
%plot(P(a:L,1),abs(yy(a:L)-P(a:L,2))./P(a:L,2),'ro-');
plot(P(a:L,1),(yy(a:L)-P(a:L,2))/2^B,'ro-');

grid on
end

function y=Residuum(c)
global P

    y = P(:,2) - Ansatzfunktion(P(:,1),c);
    %y = sqrt((c(1)-P(:,1)).^2+(c(2)-P(:,2)).^2)-c(3);

end

function y=Ansatzfunktion(x,c)

    %    y=c(1)*x.^5+c(2)*x.^4+c(3)*x.^3+c(4)*x.^2 +c(5).*x +c(6);
%    y = c(1)*exp(c(2)*x);
    %y = c(1)*x+c(2);
    %y = c(1)*x.^2+c(2)*x; 
%    y = c(3)*x.^2+c(2)*x+c(1); 
%    y = c(1)*exp(-c(2)*x)+c(3);
%    y = c(1)*exp(c(2)*x)+c(3)*x.*exp(c(4)*x);

%    y = c(1)*exp(-c(2)*x).*sin(c(3)*x+c(4));

global N

    y=c(1);
    for i=1:N
        y = y + c(i+1)*x.^i;
    end
end